Step 1: Analyse Question Stem
x is greater than zero.
We have to find if f(\(x^2\)) = \(f(x)^2\)
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCEStatement 1: f(x) = √x
f(\(x^2\)) = \(\sqrt{x^2} \)
On the GMAT, \(\sqrt{x^2}\) = |x|; this means that these are equivalent functions, taking the same inputs and giving the same outputs. Therefore,
\(\sqrt{x^2}\) = x if x ≥ 0
= -x if x < 0
Since the question data clearly says that x > 0, f(\(x^2\)) = \(\sqrt{x^2}\) = x.
\([f(x)]^2\) = \([\sqrt{x}]^2\) = x
Therefore, f(\(x^2\)) = \(f(x)^2\)The data in statement 1 is sufficient to answer the question with a definite YES.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: x = 9
We have no information about the definition of the function and therefore, a value of x is of no use in answering the question.
The data in statement 2 is insufficient to answer the question with a YES or NO.
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A. _________________
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